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You are considering buying one of two brands of barbecue grills. Brand F costs $650 and will last for about fifteen years. Brand G costs $200 and will last for about five years, so you will need to buy three of them over the years to equal one Brand F grill. In either case, you plan to pay for the grill with your credit card, which has an interest rate of 13.01%, compounded monthly. You will pay off a Brand F grill in five years of monthly payments, and you will pay off a Brand G grill in three years of monthly payments. Assuming that you have no other purchases on your credit card, over a fifteen-year period, which kind of grill will be cheaper, and how much cheaper will it be? (Round all dollar values to the nearest cent.)

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Answer:

Brand G grill will be cheaper and it will be cheaper by $159.48¢

Explanation:

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Lanuel

Based on the calculations, Brand G is more cheaper than Brand F by $159.48.

Given the following data:

  • Cost of Brand F = $650.
  • Cost of Brand G = $200.
  • Interest rate = 13.01% compounded monthly.
  • Time for Brand F = 5 years.
  • Time for Brand G = 3 years.

How to calculate monthly payment.

Mathematically, the monthly payment for an item is given by this formula:

[tex]M=P(\frac{r}{1-(1+r)^{nt}} )[/tex]

Where:

  • P is the principal.
  • r is the interest rate.
  • M is the monthly payment.
  • t is the time or number of years.
  • n is the number of times it's compounded.

Note: [tex]r=13.01=\frac{0.1301}{12} =0.01084167[/tex]

For Brand F:

Substituting the given parameters into the formula, we have;

[tex]M=650(\frac{0.01084167}{1-(1+0.01084167)^{12\times 5}} )\\\\M=650 \times 0.022758193[/tex]

M = $14.79.

For the total payment:

Total payment = [tex]14.79 \times 60[/tex]

Total payment = $887.4.

For Brand G:

[tex]M=200(\frac{0.01084167}{1-(1+0.01084167)^{12\times 3}} )\\\\M=200 \times 0.033698769[/tex]

M = $6.74.

For the total payment:

Total payment = [tex]6.74 \times 36[/tex]

Total payment = $242.64.

Since three (3) of Brand G must be purchased, we have:

New payment = [tex]242.64 \times 3[/tex]

New payment = $727.92.

Therefore, Brand G is more cheaper than Brand F.

The difference:

Difference = [tex]887.4 - 727.92[/tex]

Difference = $159.48.

Read more on interest rate here: https://brainly.com/question/24341207